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Jingdong book

浙江省级重点学科应用数学教学改革与科学研究丛书：信息论与密码学

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Jingdong book

浙江省级重点学科应用数学教学改革与科学研究丛书：信息论与密码学

Name: 浙江省级重点学科应用数学教学改革与科学研究丛书：信息论与密码学
Brand: Jingdong book
SKU: 3118192241
Price: 24.65 USD
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《浙江省级重点学科应用数学教学改革与科学研究丛书：信息论与密码学》概念清晰，推理严密，论证细致，对每部分内容，都展示是什么、为什么和怎么做的全过程，并将基础和应用并重的教育理念融人其中。全书分6章，介绍信息论和密码学的基础知识。在信息论方面，引入给出信源和信道概念的联合概率空间，并由此给出离散信源的数学模型，介绍信息量、熵和信源编码；给出离散信道的数学模型，介绍互信息、信道容量和信道编码，在密码学方面，讲述密码学的基础理论，介绍以DES系统为代表的分组密码和以RSA系统为代表的公钥密码。
《浙江省级重点学科应用数学教学改革与科学研究丛书：信息论与密码学》可作为高等院校数学和应用数学、信息与计算科学专业和信息类、软件类本科生和研究生的信息论与密码学教材和参考书。

Catalogue

总序
前言
第1章绪论
1.1 几个概念和信息论的研究内容
1.2 概率论相关知识
1.2.1 概率空间与随机变量
1.2.2 事件独立性与联合概率空间
1.2.3 离散概率空间
1.2.4 随机序列与马尔可夫链
1.2.5 伯努利试验与伯努利大数定律
1.3 凸函数与詹森不等式
习题1

第2章离散信源及其数量关系
2.1 离散信源与信息的数学模型
2.1.1 发出仅含一个符号的信息的信源
2.1.2 发出N个符号的信息的信源
2.1.3 离散信源
2.1.4 离散平稳信源
2.1.5 马尔可夫信源
2.1.6 离散平稳无记忆信源
2.2 事件的信息量
2.3 平均自信息——熵
2.3.1 熵的定义
2.3.2 熵的性质
2.3.3 离散平稳信源的极限熵
2.3.4 m阶马尔可夫信源的极限熵
2.3.5 离散平稳无记忆信源的极限熵
习题2

第3章信源编码
3.1 编码定义及相关概念
3.2 扩展编码与简单等长无错编码
3.2.1 扩展编码
3.2.2 简单等长无错编码
3.2.3 分组等长编码
3.3 离散平稳无记忆信源的等长编码
3.3.1 典型序列与渐进等分割性
3.3.2 等长编码定理
3.4 离散平稳信源的不等长编码
3.4.1 即时码的定义
3.4.2 码树与即时码的构造
3.4.3 即时码的存在定理
3.4.4 离散平稳信源的不等长编码举例及存在问题
3.5 最佳码与近似最佳码
3.5.1 平均码长
3.5.2 最佳码
3.5.3 离散平稳无记忆信源的近似最佳即时码
3.5.4 一般离散平稳信源的近似最佳即时码
3.5.5 m阶马尔可夫信源的近似最佳即时码
3.5.6 霍夫曼码
习题3

第4章离散信道及其数量关系
4.1 信道的数学模型
4.2 互信息
4.2.1 互信息的概念
4.2.2 互信息的性质
4.3 信道容量
4.3.1 信道容量的概念
4.3.2 信道容量的计算
习题4

第5章信道编码
5.1 信道编码的基础理论
5.1.1 信道编码概述
5.1.2 信道译码方式及译码准则
5.1.3 渐近等分割性与信道编码定理
5.2 群码
5.2.1 分组编码
5.2.2 群及模2运算
5.2.3 群码的构造
5.2.4 群码的应用举例
……

第6章密码学
参考文献
习题参考答案

Introduction

信息论由美国通信科学家香农（C.E.Shannon）于20世纪40年代创立。随着计算机技术的发展，信息论的研究内容与计算机的关系越来越密切。电子计算机的研制，一开始就涉及符号的编码问题，而编码则是信息论的重要研究内容。现在，计算机已离不开信息论的研究对象，同时，信息论也转为根据计算机特点进行研究。
密码学的历史比信息论长，但随着信息论的创立，密码学的基础理论得到了充实，信息论中的编码理论和技术也为密码学的发展提供了极大的支持。此外，计算机技术的发展对密码学提出新的研究课题的同时，也为密码编码和解码方法的实现提供了有力的工具。软件和网络安全问题已经成为现代人必须时刻面对的问题，而这些问题就是密码学问题，密码编码的实现已不可能由人工进行，必须借助计算机。信息论、计算机和密码学三者，已经到了必须共同发展、互相不能离开的程度。
本书介绍最基本的信息论和密码学内容，为出身数学的读者编写。因此，时刻注意概念的明确性、推理和论证的严密性，避免出现无法找到出处的概念和记号，可以用定义形式表达的概念都将其写作定义，不能用定义描述的概念尽量将其符号化。例如，信息、信道等概念，都用明确的符号加以表示，正如点、集合的概念不能给出具体的定义，但可用a，E等符号表示一样。本书中的有关结论尽量表述为定理，其证明力求严格，证明中避免使用容易引起歧义的描述性语言和“显然”等字眼，不允许用“易知”掩盖实际上困难的证明步骤，
本书的定位是教材，因此，必须在其中融人教育理念，我们认为，教育应该基础和应用并重，高等院校应该以提高学生的素质和能力为目标，而不是教学生技术和手艺，所以，不能什么“有用”就学什么，什么“没用”就不学什么。不然，学生学到的知识是零碎的、不成系统的，几年下来，学生会处于被动、应对的状态，丧失联想能力和主动的创造精神。在这种理念指引下，本书注意解释一些知识的脉络，以开阔学生的眼界，提高学生的联想能力，例如，在介绍以公理化方法给出的概率空间定义时，用一定篇幅对该方法与其他方面知识的关系做了阐述，以使学生在见到类似结构的问题时，可以借鉴来自不同方面的知识。

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